arXiv subjects

Sarah C. Millholland

Publications and source records attributed to Sarah C. Millholland.

At least 19 recordsLinked to original sources

arXiv2026

The Neptunian Final Parsec Problem: How Inertial Waves Enable Neptunes and Gas Giants to Survive Tidal Migration

Observations indicate that some hot Neptunes and Jupiters underwent high eccentricity migration (HEM). A longstanding issue facing HEM theory remains, however: in order to shrink their orbits by ${\sim}1{-}2$ orders of magnitude, planets must dissipate ${\gtrsim}10{\times}$ more orbital energy than is contained in their structural binding energy. Previous work suggests that excitation of planets' fundamental modes (''$f$-modes'') at very high eccentricities, $e{\sim}$0.99, can shrink semi-major axes by ${\sim}$an order of magnitude (${\sim}5{\rightarrow}0.5$ au) while safely bleeding tidal energy to space. We examine how planets traverse the remaining order of magnitude in orbital shrinkage, $a{\sim}$0.5${\rightarrow}$0.05 au, which still poses a danger for Neptunian planets due to their lower binding energies (their ''final parsec'' problem). To assess whether tidally-migrating Neptunes balance their energy budgets, we perform coupled orbit/structure calculations tracking their frequency-dependent tidal response under inertial waves (IWs). We show that tidal radius inflation at moderate eccentricities sweeps Neptunes' fundamental modes back into resonance with tidal forcing; only a small amount of tidal heat relative to a Neptune's binding energy is needed to drive this $f$-mode excitation. This excitation of Neptunes' $f$-modes may offer a route to safe circularization, provided the $f$-mode dissipates without harming the planet. In contrast, eccentric gas giants ($e{\sim}0.9$) circularize without drama over ${\sim}$Gyr. Our theory predicts that warm Neptunes on a HEM track ($a{\gtrsim}0.1 \ \mathrm{au}, \ e{\gtrsim}0.8$) should be rare, in opposition to warm gas giants and lower eccentricity Neptunes. Observational confirmation of our predictions would constrain the interior structures of Neptunian planets via tidal theory.

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arXiv2026

ExoMOD II. A Statistical Model of Transit Timing Variations in Kepler Multi-Planet Systems

In Paper I (Nesvorný et al. 2026), we forward modeled transit observations of the Kepler telescope to characterize the orbital properties of close-in planetary systems. The new population model, ExoMOD, was calibrated on Kepler's DR25 data. Here we use ExoMOD to statistically predict Transit Timing Variations (TTVs) from gravitationally interacting planets in the close-in systems, and compare these predictions with TTVs actually detected in the Kepler data. We find that planet-planet interactions are not expected to produce significant {\it short-period} TTVs, $P_{\rm TTV}/P_{\rm orb}<10$, where $P_{\rm TTV}$ and $P_{\rm orb}$ are the TTV and orbital periods, often enough to explain the short-period TTV signals inferred from the Kepler data. Most measured short-period signals must therefore have a different origin. The statistics of {\it long-period} TTVs -- likely arising from the gravitational interaction between planets -- indicates that single transiting planets have TTV-inducing companions nearly as often as doubles, thus ruling out multiplicity distributions with a prevalence of intrinsic singles. The fraction of planets with measured long-period TTVs increases to $\simeq 15$-18\% for observed multiplicities $m \geq 3$, suggesting a change in the orbital architecture. High-multiplicity planetary systems have low gap complexities and probably retained a memory of their formation conditions. Ultimately, our work aims at developing a more informative feedback between observations and planet formation theories.

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arXiv2026

The Architecture of the 14 Herculis System Suggests Primordial Ejection of a Massive Planet

The 14 Herculis system hosts two super-Jupiters on eccentric, significantly misaligned orbits. This orbital architecture represents a dynamical puzzle that demands explanation. In this work, we reproduce the system's dynamical history and current architecture using a large suite of N-body simulations of planet-planet scattering. Our results demonstrate that planet-planet scattering is able to reproduce 14 Her's peculiar orbital architecture, but only if additional massive bodies were initially present in the system that were subsequently ejected. The mass of any such ejected planet can in turn constrain the system's initial configuration. We also analyze the present-day secular evolution of the system and conclude that while there are most likely nontrivial eccentricity and inclination oscillations currently occurring, the magnitudes of these oscillations are not strong enough to allow tidal forces to meaningfully alter the system's architecture. Finally, we discuss how forthcoming observations from future Gaia data releases and the Roman mission may situate 14 Her's dynamical history within a broader, population-level framework.

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arXiv2026

Direct Imaging Constraints on Binary Planets and Exomoons around Epsilon Indi A b

Epsilon Indi A b is a directly imaged $\sim6 M_{\rm Jup}$ exoplanet orbiting a nearby (3.6 pc) K-dwarf at $\sim 30$ AU. We analyze archival JWST/MIRI 15 $μ$m coronagraphic imaging of this planet to search for directly imaged satellites orbiting Eps Ind A b. Within the planet's Hill sphere (radius $R_H \approx 2.3$ AU or $1.3 λ/D$), we compare single- and double-PSF models using Bayesian evidence. We find that a double-PSF (binary planet) fit is preferred. This apparent preference can most plausibly be explained by systematics, although follow-up observations would be required to fully rule out a binary planet interpretation. We construct a contrast curve of the exoplanet after removing this feature, demonstrating sensitivity to companions as faint as $0.03\times$ the F1550C flux of Eps Ind A b (equivalent to $T = 130$ K, $1.3 M_{\rm Jup}$) at large separations (>2 AU). We also demonstrate sensitivity to brighter companions $0.2\times$ the F1550C flux of Eps Ind A b (equivalent to $T = 180$ K, $2.5 M_{\rm Jup}$) down to separations of 0.52 AU (1.3 pixels; $0.29 λ/D$; 144 mas). This study demonstrates that JWST/MIRI can directly detect exomoons or binary planets inside the Hill sphere of directly imaged exoplanets orbiting neighboring stars.

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arXiv2026

Self-consistent Dynamical and Chaotic Tides in the REBOUNDx framework

At high eccentricities, tidal forcing excites vibrational modes within orbiting bodies known as dynamical tides. In this paper, we implement the coupled evolution of these modes with the body's orbit in the \texttt{REBOUNDx} framework, an extension to the popular $N$-body integrator \texttt{REBOUND}. We provide a variety of test cases relevant to exoplanet dynamics and demonstrate overall agreement with prior studies of dynamical tides in the secular regime. Our implementation is readily applied to various high-eccentricity scenarios and allows for fast and accurate $N$-body investigations of astrophysical systems for which dynamical tides are relevant.

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arXiv2025

Exploring Exoplanet Dynamics with JWST: Tides, Rotation, Rings, and Moons

Although nearly 6,000 exoplanets are currently known, in most cases our knowledge is limited to a handful of the planet's orbital characteristics and bulk properties such as radius and mass. The James Webb Space Telescope (JWST) can expand our knowledge not only by probing exoplanet atmospheres, but also by measuring additional orbital and physical properties of exoplanets, thanks to its superior light-gathering power and measurement precision. Here, we describe the potential of JWST to unveil dynamical phenomena that were previously beyond our reach, such as tidal distortion and inflation, rotational flattening, planetary rings, and moons.

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arXiv2025

Planetary Obliquity Excitation Through Pre-Main Sequence Stellar Evolution

A planet's axial tilt ("obliquity") substantially affects its atmosphere and habitability. It is thus essential to comprehend the various mechanisms that can excite planetary obliquities, particularly at the primordial stage. Here, we explore planetary obliquity excitation induced by the early evolution of the host star. A young, distended star spins rapidly, resulting in a large gravitational quadrupole moment that induces nodal recession of the planet's orbit. As the star contracts and spins down, the nodal recession frequency decreases and can cross the planet's spin axis precession frequency. An adiabatic encounter results in the planet's capture into a secular spin-orbit resonance and excites the obliquity to large values. We find planets within $a \lesssim 1 \ \mathrm{AU}$ are most affected, but adiabatic capture depends on the initial stellar radius and spin rate. The overall picture is complicated by other sources of perturbation, including the disk, multiple planets, and tidal dissipation. Tides make it such that stellar oblateness-induced obliquity excitation is transient since tidal perturbations cause the resonance to break once high obliquities are reached. However, this early transient excitation is important because it can prime planets for long-term capture in a secular spin-orbit resonance induced by planet-planet interactions. Thus, although stellar oblateness-induced resonances are short-lived, they facilitate the prevalence of long-lived non-zero obliquities in exoplanets.

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arXiv2025

Planetary Edge Trends (PET). I. The Inner Edge-Stellar Mass Correlation

The position of the innermost planet (i.e., the inner edge) in a planetary system provides important information about the relationship of the entire system to its host star properties, offering potentially valuable insights into planetary formation and evolution processes. In this work, based on the Kepler Data Release 25 (DR25) catalog combined with LAMOST and Gaia data, we investigate the correlation between stellar mass and the inner edge position across different populations of small planets in multi-planetary systems, such as super-Earths and sub-Neptunes. By correcting for the influence of stellar metallicity and analyzing the impact of observational selection effects, we confirm the trend that as stellar mass increases, the position of the inner edge shifts outward. Our results reveal a stronger correlation between the inner edge and stellar mass with a power-law index of 0.6-1.1, which is larger compared to previous studies. The stronger correlation in our findings is primarily attributed to two factors: first, the metallicity correction applied in this work enhances the correlation; second, the previous use of occurrence rates to trace the inner edge weakens the observed correlation. Through comparison between observed statistical results and current theoretical models, we find that the pre-main-sequence (PMS) dust sublimation radius of the protoplanetary disk best matches the observed inner edge stellar mass. Therefore, we conclude that the inner dust disk likely limits the innermost orbits of small planets, contrasting with the inner edges of hot Jupiters, which are associated with the magnetospheres of gas disks, as suggested by previous studies. This highlights that the inner edges of different planetary populations are likely regulated by distinct mechanisms.

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arXiv2025

Empirical Constraints on Tidal Dissipation in Exoplanet Host Stars

The orbits of short-period exoplanets are sculpted by tidal dissipation. However, the mechanisms and associated efficiencies of these tidal interactions are poorly constrained. We present robust constraints on the tidal quality factors of short-period exoplanetary host stars through the usage of a novel empirical technique. The method is based on analyzing structures in the population-level distribution of tidal decay times, defined as the time remaining before a planet spirals into its host star due to stellar tides. Using simple synthetic planet population simulations and analytic theory, we show that there exists a steady-state portion of the decay time distribution with an approximately power-law form. This steady-state feature is clearly evident in the decay time distribution of the observed short-period planet population. We use this to constrain both the magnitude and frequency dependence of the stellar tidal quality factor and show that it must decrease sharply with planetary orbital period. Specifically, with $Q_{\star}' = Q_0 (P/2 \ \mathrm{days})^α$, we find $10^{5.5} \lesssim Q_0 \lesssim 10^7$ and $-4.33 \lesssim α\lesssim -2$. Our results are most consistent with predictions from tidal resonance locking, in which the planets are locked into resonance with a tidally excited gravity mode in their host stars.

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arXiv2024

Planet-Planet Scattering and ZLK Migration -- The Dynamical History of HAT-P-11

The two planets of the HAT-P-11 system represent fascinating dynamical puzzles due to their significant eccentricities and orbital misalignments. In particular, HAT-P-11 b is on a close-in orbit that tides should have circularized well within the age of the system. Here we propose a two-step dynamical process that can reproduce all intriguing aspects of the system. We first invoke planet-planet scattering to generate significant eccentricities and mutual inclinations between the planets. We then propose that this misalignment initiated von-Zeipel-Lidov-Kozai cycles and high-eccentricity migration that ultimately brought HAT-P-11 b to its present-day orbit. We find that this scenario is fully consistent only when significant tidally-driven radius inflation is accounted for during the tidal migration. We present a suite of N-body simulations exploring each phase of evolution and show that this scenario is consistent with all observational posteriors and the reported age of the system.

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arXiv2024

The Prevalence of Resonance Among Young, Close-in Planets

Multiple planets undergoing disk migration may be captured into a chain of mean-motion resonances with the innermost planet parked near the disk's inner edge. Subsequent dynamical evolution may disrupt these resonances, leading to the non-resonant configurations typically observed among {\it Kepler} planets that are Gyrs old. In this scenario, resonant configurations are expected to be more common in younger systems. This prediction can now be tested, thanks to recent discoveries of young planets, particularly those in stellar clusters, by NASA's {\it TESS} mission. We divided the known planetary systems into three age groups: young ($<$100-Myr-old), adolescent (0.1-1-Gyr-old), and mature ($>1$-Gyr-old). The fraction of neighboring planet pairs having period ratios within a few percent of a first-order commensurability (e.g.~4:3, 3:2, or 2:1) is 70$\pm$15\% for young pairs, 24$\pm$8\% for adolescent pairs, and 15$\pm$2\% for mature pairs. The fraction of systems with at least one nearly commensurable pair (either first or second-order) is 86$\pm13$\% among young systems, 38$\pm12$\% for adolescent systems, and 23$\pm3$\% for mature systems. First-order commensurabilities prevail across all age groups, with an admixture of second-order commensurabilities. Commensurabilities are more common in systems with high planet multiplicity and low mutual inclinations. Observed period ratios often deviate from perfect commensurability by $\sim$1\% even among young planets, too large to be explained by resonant repulsion with equilibrium eccentricity tides. We also find that super-Earths in the radius gap ($1.5-1.9R_\oplus$) are less likely to be near-resonant (11.9$\pm2.0\%$) compared to Earth-sized planets ($R_p<1R_\oplus$; 25.3$\pm4.4\%$) or mini-Neptunes ($1.9R_\oplus \leq R_p<2.5R_\oplus$; 14.4$\pm1.8\%$).

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arXiv2024

TOI-1685 b is a Hot Rocky Super-Earth: Updates to the Stellar and Planet Parameters of a Popular JWST Cycle 2 Target

We present an updated characterization of the TOI-1685 planetary system, which consists of a P$_{\rm{b}}$ = 0.69\,day USP super-Earth planet orbiting a nearby ($d$ = 37.6\,pc) M2.5V star (TIC 28900646, 2MASS J04342248+4302148). This planet was previously featured in two contemporaneous discovery papers, but the best-fit planet mass, radius, and bulk density values were discrepant allowing it to be interpreted either as a hot, bare rock or a 50\% H$_{2}$O / 50\% MgSiO$_{3}$ water world. TOI-1685 b will be observed in three independent JWST cycle two programs, two of which assume the planet is a water world while the third assumes that it is a hot rocky planet. Here we include a refined stellar classification with a focus on addressing the host star's metallicity, an updated planet radius measurement that includes two sectors of TESS data and multi-color photometry from a variety of ground-based facilities, and a more accurate dynamical mass measurement from a combined CARMENES, IRD, and MAROON-X radial velocity data set. We find that the star is very metal-rich ([Fe/H] $\simeq$ +0.3) and that the planet is systematically smaller, lower mass, and higher density than initially reported, with new best-fit parameters of \Rpl = 1.468 $^{+0.050}_{-0.051}$ \Rearth\ and \Mpl = 3.03$^{+0.33}_{-0.32}$ \Mearth. These results fall in between the previously derived values and suggest that TOI-1685 b is a hot, rocky, planet with an Earth-like density (\Rhopl = 5.3 $\pm$ 0.8 g cm$^{-3}$, or 0.96 \rhoearth), high equilibrium temperature (T$_{\rm{eq}}$ = 1062 $\pm$ 27 K) and negligible volatiles, rather than a water world.

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arXiv2024

The black hole low mass X-ray binary V404 Cygni is part of a wide hierarchical triple, and formed without a kick

Evidence suggests that when compact objects such as black holes and neutron stars form, they may receive a ``natal kick,'' where the stellar remnant gains momentum. Observational evidence for neutron star kicks is substantial, yet limited for black hole natal kicks, and some proposed black hole formation scenarios result in very small kicks. Here, we report the discovery that the canonical black hole low-mass X-ray binary V404 Cygni is part of a wide hierarchical triple with a tertiary companion at least 3500 astronomical units away from the inner binary. Given the orbital configuration, the black hole likely received a sub-5 kilometer per second kick to have avoided unbinding the tertiary. This discovery reveals that at least some black holes form with nearly no natal kick. Furthermore, the tertiary in this system lends credence to evolutionary models of low-mass X-ray binaries involving a hierarchical triple structure. Remarkably, the tertiary is evolved, indicating that the system formed 3-5 billion years ago, and that the black hole has removed at least half a solar mass of matter from its evolved secondary companion. During the event in which the black hole formed, it is likely that at least half of the mass of the black hole progenitor collapsed into the black hole; it may even have undergone a complete implosion, enabling the tertiary to remain loosely bound.

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arXiv2023

Spin Dynamics of Planets in Resonant Chains

About a dozen exoplanetary systems have been discovered with three or more planets participating in a sequence of mean-motion resonances. The unique and complex architectures of these so-called "resonant chains" motivate efforts to characterize their planets holistically. In this work, we perform a comprehensive exploration of the spin-axis dynamics of planets in resonant chains. Planetary spin states are closely linked with atmospheric dynamics and habitability and are thus especially relevant to resonant chains like TRAPPIST-1, which hosts several temperate planets. Considering a set of observed resonant chains, we calculate the equilibrium states of the planetary axial tilts ("obliquities"). We show that high obliquity states exist for $\sim60\%$ of planets in our sample, and many of these states can be stable in the presence of tidal dissipation. Using case studies of two observed systems (Kepler-223 and TOI-1136), we demonstrate how these high obliquity states could have been attained during the initial epoch of disk-driven orbital migration that established the resonant orbital architectures. We show that the TRAPPIST-1 planets most likely have zero obliquities, with the possible exception of planet d. Overall, our results highlight that both the orbital and spin states of resonant chains are valuable relics of the early stages of planet formation and evolution.

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arXiv2023

Can Cold Jupiters Sculpt the Edge-of-the-Multis?

Compact systems of multiple close-in super-Earths/sub-Neptunes ("compact multis") are a ubiquitous outcome of planet formation. It was recently discovered that the outer edges of compact multis are located at smaller orbital periods than expected from geometric and detection biases alone, suggesting some truncation or transition in the outer architectures. Here we test whether this "edge-of-the-multis" might be explained in any part by distant giant planets in the outer regions ($\gtrsim 1$ AU) of the systems. We investigate the dynamical stability of observed compact multis in the presence of hypothetical giant ($\gtrsim 0.5 \ M_{\mathrm{Jup}}$) perturbing planets. We identify what parameters would be required for hypothetical perturbing planets if they were responsible for dynamically sculpting the outer edges of compact multis. "Edge-sculpting" perturbers are generally in the range $P\sim100-500$ days for the average compact multi, with most between $P\sim200-300$ days. Given the relatively close separation, we explore the detectability of the hypothetical edge-sculpting perturbing planets, finding that they would be readily detectable in transit and radial velocity data. We compare to observational constraints and find it unlikely that dynamical sculpting from distant giant planets contributes significantly to the edge-of-the-multis. However, this conclusion could be strengthened in future work by a more thorough analysis of the detection yields of the perturbing planets.

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arXiv2023

A 2:1 Mean-Motion Resonance Super-Jovian pair revealed by TESS, FEROS, and HARPS

We report the discovery of a super-Jovian 2:1 mean-motion resonance (MMR) pair around the G-type star TIC 279401253, whose dynamical architecture is a prospective benchmark for planet formation and orbital evolution analysis. The system was discovered thanks to a single transit event recorded by the Transiting Exoplanet Survey Satellite (TESS) mission, which pointed to a Jupiter-sized companion with poorly constrained orbital parameters. We began ground-based precise radial velocity (RV) monitoring with HARPS and FEROS within the Warm gIaNts with tEss (WINE) survey to constrain the transiting body's period, mass, and eccentricity. The RV measurements revealed not one but two massive planets with periods of 76.80$_{-0.06}^{+0.06}$ days and 155.3$_{-0.7}^{+0.7}$ days, respectively. A combined analysis of transit and RV data yields an inner transiting planet with a mass of 6.14$_{-0.42}^{+0.39}$ M$_{\rm Jup}$ and a radius of 1.00$_{-0.04}^{+0.04}$ R$_{\rm Jup}$, and an outer planet with a minimum mass of 8.02$_{-0.18}^{+0.18}$ M$_{\rm Jup}$, indicating a massive giant pair. A detailed dynamical analysis of the system reveals that the planets are locked in a strong first-order, eccentricity-type 2:1 MMR, which makes TIC 279401253 one of the rare examples of truly resonant architectures supporting disk-induced planet migration. The bright host star, $V \approx$ 11.9 mag, the relatively short orbital period ($P_{\rm b}$ = 76.80$_{-0.06}^{+0.06}$ d) and pronounced eccentricity (e =0.448$_{-0.029}^{+0.028}$) make the transiting planet a valuable target for atmospheric investigation with the James Webb Space Telescope (JWST) and ground-based extremely-large telescopes.

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arXiv2023

Self-Consistent Spin, Tidal and Dynamical Equations of Motion in the REBOUNDx Framework

We have introduced self-consistent spin, tidal and dynamical equations of motion into REBOUNDx, a library of additional effects for the popular N-body integrator REBOUND. The equations of motion used are derived from the constant time lag approximation to the equilibrium tide model of tidal friction. These effects will allow the study of a variety of systems where the full dynamical picture cannot be encapsulated by point particle dynamics. We provide several test cases and benchmark the code's performance against analytic predictions. The open-source code is available in the most recent release of REBOUNDx.

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arXiv2022

Measured Spin-Orbit Alignment of Ultra-Short Period Super-Earth 55 Cancri e

A planet's orbital alignment places important constraints on how a planet formed and consequently evolved. The dominant formation pathway of ultra-short period planets ($P<1$ day) is particularly mysterious as such planets most likely formed further out, and it is not well understood what drove their migration inwards to their current positions. Measuring the orbital alignment is difficult for smaller super-Earth/sub-Neptune planets, which give rise to smaller amplitude signals. Here we present radial velocities across two transits of 55 Cancri e, an ultra-short period Super-Earth, observed with the Extreme Precision Spectrograph (EXPRES). Using the classical Rossiter-McLaughlin (RM) method, we measure 55 Cnc e's sky-projected stellar spin-orbit alignment (i.e., the projected angle between the planet's orbital axis and its host star's spin axis) to be $λ=10\substack{+17\\ -20}^{\circ}$ with an unprojected angle of $ψ=23\substack{+14\\ -12}^{\circ}$. The best-fit RM model to the EXPRES data has a radial velocity semi-amplitude of just $0.41\substack{+0.09\\ -0.10} m s^{-1}$. The spin-orbit alignment of 55 Cnc e favors dynamically gentle migration theories for ultra-short period planets, namely tidal dissipation through low-eccentricity planet-planet interactions and/or planetary obliquity tides.

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